How can i center axis on the object?
Option 1: 


Select your object (not edit mode)
Press Ctrl+Shift+Alt+C (Yes, 4 keys at once)
Select "Origin to Geometry"


Option 2: 


Select your object and go into edit mode
Press A (maybe twice) to select your whole mesh. 
Press G to grab your selection and move it to your Origin. 
(If you only want to move it straight down press Z to stick the movement to the Z-axis


Note that if you want to move your object around in your scene you should not do that in edit mode as the origin (the thing in the yellow circle) doesn't move with it. Otherwise you end up with the problem you hae right now.